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AP EAMCET · Maths · Straight Lines

If \(C\) is the mid-point of the line segment \(\mathbf{A B}\) and \(P\) is any point outside the line \(A B\), then

  1. A \(P A+P B+2 P C=0\)
  2. B \(P A+P B+P C=0\)
  3. C \(P A+P B=2 P C\)
  4. D \(P A+P B=P C\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(P A+P B=2 P C\)

Step-by-step Solution

Detailed explanation

\(\mathbf{P A}+\mathbf{A C}=\mathbf{P C}\) ...(i) \(\mathbf{P B}+\mathbf{B C}=\mathbf{P C}\) ...(ii) On adding Eqs. (i) and (ii), \(\overrightarrow{\mathbf{P A}}+\overrightarrow{\mathbf{P B}}+\overrightarrow{\mathbf{A C}}+\overrightarrow{\mathbf{B C}}=2 \mathbf{P C}\)…